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Номер 252, страница 31 - гдз по физике 7-9 класс сборник задач Московкина, Волков
Авторы: Московкина Е. Г., Волков В. А.
Тип: Сборник задач
Издательство: ВАКО
Год издания: 2011 - 2026
Цвет обложки: синий
ISBN: 978-5-408-00459-1
Популярные ГДЗ в 7 классе
7 класс. Сообщающиеся сосуды - номер 252, страница 31.
App\Models\Task {#1030 // resources/views/models/task/default.blade.php #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1425063 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "31" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/7-252" "field_display_title" => "252" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ 0 => App\Models\Term {#1036 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #original: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1046 #items: array:1 [ 0 => App\Models\Branch {#1045 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1424761 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "7 класс" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1047 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "4" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1057 #items: array:1 [ 0 => App\Models\Book {#1056 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 4994 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1061 #items: array:1 [ 0 => App\Models\Term {#1058 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #original: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1064 #items: array:3 [ 0 => App\Models\Term {#1060 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5456 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "7" "field_cases" => array:6 [ "field_accusative_case" => "седьмой" "field_creative_case" => "седьмым" "field_dative_case" => "седьмому" "field_genitive_case" => "седьмого" "field_nominative_case" => "седьмой" "field_prepositional_case" => "седьмом" ] "field_translit" => "sedmoj" ] #original: array:6 [ "id" => 5456 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "7" "field_cases" => array:6 [ "field_accusative_case" => "седьмой" "field_creative_case" => "седьмым" "field_dative_case" => "седьмому" "field_genitive_case" => "седьмого" "field_nominative_case" => "седьмой" "field_prepositional_case" => "седьмом" ] "field_translit" => "sedmoj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Term {#1062 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5457 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "8" "field_cases" => array:6 [ "field_accusative_case" => "восьмой" "field_creative_case" => "восьмым" "field_dative_case" => "восьмому" "field_genitive_case" => "восьмого" "field_nominative_case" => "восьмой" "field_prepositional_case" => "восьмом" ] "field_translit" => "vosmoj" ] #original: array:6 [ "id" => 5457 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "8" "field_cases" => array:6 [ "field_accusative_case" => "восьмой" "field_creative_case" => "восьмым" "field_dative_case" => "восьмому" "field_genitive_case" => "восьмого" "field_nominative_case" => "восьмой" "field_prepositional_case" => "восьмом" ] "field_translit" => "vosmoj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Term {#1059 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "field_translit" => "devjatyj" ] #original: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "field_translit" => "devjatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1067 #items: array:1 [ 0 => App\Models\Term {#1065 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5227 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ВАКО" "field_cases" => null "field_translit" => "vako" ] #original: array:6 [ "id" => 5227 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ВАКО" "field_cases" => null "field_translit" => "vako" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1063 #items: array:2 [ 0 => App\Models\Term {#1077 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 5285 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Московкина" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Елена" "field_patronymic" => "Геннадьевна" "field_surname_rp" => null ] #original: array:12 [ "id" => 5285 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Московкина" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Елена" "field_patronymic" => "Геннадьевна" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Term {#1076 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4026 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Волков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Владимир" "field_patronymic" => "Анатольевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 4026 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Волков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Владимир" "field_patronymic" => "Анатольевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1073 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1071 #items: array:1 [ 0 => App\Models\Term {#1068 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6598 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Сборник задач" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "сборник задач" "field_creative_case" => "сборником задач" "field_dative_case" => "сборнику задач" "field_genitive_case" => "сборника задач" "field_nominative_case" => "сборник задач" "field_prepositional_case" => "сборнике задач" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "sbornik zadach" ] #original: array:10 [ "id" => 6598 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Сборник задач" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "сборник задач" "field_creative_case" => "сборником задач" "field_dative_case" => "сборнику задач" "field_genitive_case" => "сборника задач" "field_nominative_case" => "сборник задач" "field_prepositional_case" => "сборнике задач" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "sbornik zadach" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1072 #items: array:1 [ 0 => App\Models\Term {#1075 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "rossiya" ] #original: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "rossiya" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1078 #items: array:1 [ 0 => App\Models\Term {#1069 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "moskva" ] #original: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "moskva" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1070 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1066 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1079 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1080 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1081 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1082 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2011" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => null "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => null "field_default_folder" => "/fizika_07/moskovkina-sz/" "field_isbn" => "978-5-408-00459-1" "field_cover" => array:1 [ 0 => "/media/fizika_07/moskovkina-sz/covers/cover1.webp?ts=1758729953" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_07/moskovkina-sz/covers/cover1.webp?ts=1758729953" "alt" => "" "width" => "1466" "height" => "2407" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1083 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1084 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1085 #items: [] #escapeWhenCastingToString: false } "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1095 #items: array:1 [ 0 => App\Models\Term {#1094 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "siniy" ] #original: array:6 [ "id" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "siniy" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 378 "subject" => 556 "class_subject" => 491 ] ] #original: array:50 [ "id" => 4994 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1061} "field_class" => Illuminate\Database\Eloquent\Collection {#1064} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1067} "field_author" => Illuminate\Database\Eloquent\Collection {#1063} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1073} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1071} "field_country" => Illuminate\Database\Eloquent\Collection {#1072} "field_city" => Illuminate\Database\Eloquent\Collection {#1078} "field_series" => Illuminate\Database\Eloquent\Collection {#1070} "field_umk" => Illuminate\Database\Eloquent\Collection {#1066} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1079} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1080} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1081} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1082} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2011" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => null "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => null "field_default_folder" => "/fizika_07/moskovkina-sz/" "field_isbn" => "978-5-408-00459-1" "field_cover" => array:1 [ 0 => "/media/fizika_07/moskovkina-sz/covers/cover1.webp?ts=1758729953" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_07/moskovkina-sz/covers/cover1.webp?ts=1758729953" "alt" => "" "width" => "1466" "height" => "2407" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1083} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1084} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1085} "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1095} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 378 "subject" => 556 "class_subject" => 491 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1049 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1424761 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "7 класс" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1047} "field_page_start" => "4" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1057} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1049} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1112 #items: array:2 [ 0 => App\Models\Branch {#1120 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1424761 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "7 класс" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1121 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "4" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1122 #items: array:1 [ 0 => App\Models\Book {#1056} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1123 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1424761 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "7 класс" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1121} "field_page_start" => "4" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1122} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1123} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Branch {#1124 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1424770 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Сообщающиеся сосуды" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1125 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "29" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1126 #items: array:1 [ 0 => App\Models\Book {#1056} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1127 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1424770 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Сообщающиеся сосуды" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1125} "field_page_start" => "29" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1126} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1127} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1038 #items: array:2 [ 0 => App\Models\Element {#1103 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 1677596 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1091 #items: array:1 [ 0 => App\Models\Edition {#1090 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 6044 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1089 #items: array:1 [ 0 => App\Models\Term {#1065} ] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1054 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1052 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1088 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6044 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1089} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1054} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1052} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1088} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1425063" "type" => "task" ] "text" => "<p><strong>252.</strong> В сообщающиеся сосуды, площади поперечного сечения которых относятся как 1 : 2, налита вода. В узкий сосуд поверх воды долили столб керосина высотой 30 см. На сколько сантиметров повысится уровень воды в широком сосуде?</p>" "img" => array:1 [ 0 => array:5 [ "name" => "252-1.jpg" "alt" => null "width" => "2585" "height" => 656 "path" => "/media/fizika_07/moskovkina-sz/0-7/252-1.webp?ts=1758885527" ] ] ] #original: array:7 [ "id" => 1677596 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1091} "task" => array:2 [ "refs" => "1425063" "type" => "task" ] "text" => "<p><strong>252.</strong> В сообщающиеся сосуды, площади поперечного сечения которых относятся как 1 : 2, налита вода. В узкий сосуд поверх воды долили столб керосина высотой 30 см. На сколько сантиметров повысится уровень воды в широком сосуде?</p>" "img" => array:1 [ 0 => array:5 [ "name" => "252-1.jpg" "alt" => null "width" => "2585" "height" => 656 "path" => "/media/fizika_07/moskovkina-sz/0-7/252-1.webp?ts=1758885527" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Element {#1101 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1781444 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1051 #items: array:1 [ 0 => App\Models\Edition {#1041 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 6518 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1113 #items: array:1 [ 0 => App\Models\Term {#1115 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 7012 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Gemini 2.5 Pro" "field_cases" => array:6 [ …6] "field_translit" => "gemini 2.5 pro" ] #original: array:6 [ "id" => 7012 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Gemini 2.5 Pro" "field_cases" => array:6 [ …6] "field_translit" => "gemini 2.5 pro" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1110 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1040 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1053 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6518 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1113} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1110} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1040} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1053} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1425063" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Отношение площадей поперечного сечения сосудов: $S_1/S_2 = 1/2$</p><p>Высота столба керосина: $h_к = 30$ см</p><p>Плотность воды (табличное значение): $\rho_в = 1000$ кг/м³</p><p>Плотность керосина (табличное значение): $\rho_к = 800$ кг/м³</p><p>$h_к = 30 \text{ см} = 0.3 \text{ м}$</p><p><strong>Найти:</strong></p><p>Высоту, на которую поднимется уровень воды в широком сосуде: $\Delta h_2$</p><p><strong>Решение:</strong></p><p>Пусть $S_1$ - площадь поперечного сечения узкого сосуда, а $S_2$ - широкого. По условию $S_2 = 2S_1$.</p><p>Когда в узкий сосуд доливают керосин, он вытесняет воду. Уровень воды в узком сосуде опустится на величину $\Delta h_1$, а в широком – поднимется на величину $\Delta h_2$. Поскольку объем воды сохраняется, объем воды, ушедшей из узкого сосуда, равен объему воды, прибывшей в широкий сосуд.</p><p>$V_1 = V_2$</p><p>$S_1 \cdot \Delta h_1 = S_2 \cdot \Delta h_2$</p><p>Подставим соотношение площадей $S_2 = 2S_1$:</p><p>$S_1 \cdot \Delta h_1 = 2S_1 \cdot \Delta h_2$</p><p>Отсюда находим связь между изменениями уровней воды:</p><p>$\Delta h_1 = 2 \Delta h_2$</p><p>После установления равновесия, согласно закону сообщающихся сосудов, давление на одном и том же горизонтальном уровне в жидкости должно быть одинаковым. Выберем в качестве такого уровня конечный уровень воды в узком сосуде (то есть границу раздела керосина и воды).</p><p>Давление на этом уровне в узком сосуде создается столбом керосина высотой $h_к$:</p><p>$p_1 = \rho_к g h_к$</p><p>Давление на этом же уровне в широком сосуде создается столбом воды, высота которого равна разности уровней воды в широком и узком сосудах. Эта разность равна $H = \Delta h_1 + \Delta h_2$.</p><p>$p_2 = \rho_в g H = \rho_в g (\Delta h_1 + \Delta h_2)$</p><p>В состоянии равновесия давления равны: $p_1 = p_2$.</p><p>$\rho_к g h_к = \rho_в g (\Delta h_1 + \Delta h_2)$</p><p>Сократим на $\text{g}$:</p><p>$\rho_к h_к = \rho_в (\Delta h_1 + \Delta h_2)$</p><p>Мы получили систему из двух уравнений:</p><p>$\begin{cases} \Delta h_1 = 2 \Delta h_2 \\ \rho_к h_к = \rho_в (\Delta h_1 + \Delta h_2) \end{cases}$</p><p>Подставим первое уравнение во второе:</p><p>$\rho_к h_к = \rho_в (2\Delta h_2 + \Delta h_2)$</p><p>$\rho_к h_к = 3\rho_в \Delta h_2$</p><p>Выразим искомую величину $\Delta h_2$:</p><p>$\Delta h_2 = \frac{\rho_к h_к}{3\rho_в}$</p><p>Подставим числовые значения в систему СИ:</p><p>$\Delta h_2 = \frac{800 \text{ кг/м³} \cdot 0.3 \text{ м}}{3 \cdot 1000 \text{ кг/м³}} = \frac{240}{3000} \text{ м} = 0.08 \text{ м}$</p><p>Переведем результат в сантиметры:</p><p>$0.08 \text{ м} = 8 \text{ см}$</p><p><strong>Ответ:</strong> уровень воды в широком сосуде повысится на 8 см.</p>" ] #original: array:6 [ "id" => 1781444 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1051} "task" => array:2 [ "refs" => "1425063" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Отношение площадей поперечного сечения сосудов: $S_1/S_2 = 1/2$</p><p>Высота столба керосина: $h_к = 30$ см</p><p>Плотность воды (табличное значение): $\rho_в = 1000$ кг/м³</p><p>Плотность керосина (табличное значение): $\rho_к = 800$ кг/м³</p><p>$h_к = 30 \text{ см} = 0.3 \text{ м}$</p><p><strong>Найти:</strong></p><p>Высоту, на которую поднимется уровень воды в широком сосуде: $\Delta h_2$</p><p><strong>Решение:</strong></p><p>Пусть $S_1$ - площадь поперечного сечения узкого сосуда, а $S_2$ - широкого. По условию $S_2 = 2S_1$.</p><p>Когда в узкий сосуд доливают керосин, он вытесняет воду. Уровень воды в узком сосуде опустится на величину $\Delta h_1$, а в широком – поднимется на величину $\Delta h_2$. Поскольку объем воды сохраняется, объем воды, ушедшей из узкого сосуда, равен объему воды, прибывшей в широкий сосуд.</p><p>$V_1 = V_2$</p><p>$S_1 \cdot \Delta h_1 = S_2 \cdot \Delta h_2$</p><p>Подставим соотношение площадей $S_2 = 2S_1$:</p><p>$S_1 \cdot \Delta h_1 = 2S_1 \cdot \Delta h_2$</p><p>Отсюда находим связь между изменениями уровней воды:</p><p>$\Delta h_1 = 2 \Delta h_2$</p><p>После установления равновесия, согласно закону сообщающихся сосудов, давление на одном и том же горизонтальном уровне в жидкости должно быть одинаковым. Выберем в качестве такого уровня конечный уровень воды в узком сосуде (то есть границу раздела керосина и воды).</p><p>Давление на этом уровне в узком сосуде создается столбом керосина высотой $h_к$:</p><p>$p_1 = \rho_к g h_к$</p><p>Давление на этом же уровне в широком сосуде создается столбом воды, высота которого равна разности уровней воды в широком и узком сосудах. Эта разность равна $H = \Delta h_1 + \Delta h_2$.</p><p>$p_2 = \rho_в g H = \rho_в g (\Delta h_1 + \Delta h_2)$</p><p>В состоянии равновесия давления равны: $p_1 = p_2$.</p><p>$\rho_к g h_к = \rho_в g (\Delta h_1 + \Delta h_2)$</p><p>Сократим на $\text{g}$:</p><p>$\rho_к h_к = \rho_в (\Delta h_1 + \Delta h_2)$</p><p>Мы получили систему из двух уравнений:</p><p>$\begin{cases} \Delta h_1 = 2 \Delta h_2 \\ \rho_к h_к = \rho_в (\Delta h_1 + \Delta h_2) \end{cases}$</p><p>Подставим первое уравнение во второе:</p><p>$\rho_к h_к = \rho_в (2\Delta h_2 + \Delta h_2)$</p><p>$\rho_к h_к = 3\rho_в \Delta h_2$</p><p>Выразим искомую величину $\Delta h_2$:</p><p>$\Delta h_2 = \frac{\rho_к h_к}{3\rho_в}$</p><p>Подставим числовые значения в систему СИ:</p><p>$\Delta h_2 = \frac{800 \text{ кг/м³} \cdot 0.3 \text{ м}}{3 \cdot 1000 \text{ кг/м³}} = \frac{240}{3000} \text{ м} = 0.08 \text{ м}$</p><p>Переведем результат в сантиметры:</p><p>$0.08 \text{ м} = 8 \text{ см}$</p><p><strong>Ответ:</strong> уровень воды в широком сосуде повысится на 8 см.</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1425064" "type" => "task" ] "previous" => array:2 [ "refs" => "1425062" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1106 #items: array:1 [ 0 => App\Models\Book {#1056} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1042 #items: array:1 [ 0 => App\Models\BookPage {#1108 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 1426134 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "31" "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/page-31" "field_display_title" => "31" "field_folder" => "1" "field_image_name" => "31" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1102 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1096 #items: array:1 [ 0 => App\Models\Book {#1056} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1100 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1114 #items: array:1 [ 0 => App\Models\Element {#1116 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1678666 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1129 #items: array:1 [ 0 => App\Models\Edition {#1090} ] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1426134" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "31-1.jpg" "alt" => null "width" => "2962" "height" => 4897 "path" => "/media/fizika_07/moskovkina-sz/0-1/31-1.webp?ts=1758886608" ] ] ] #original: array:6 [ "id" => 1678666 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1129} "book_page" => array:2 [ "refs" => "1426134" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "31-1.jpg" "alt" => null "width" => "2962" "height" => 4897 "path" => "/media/fizika_07/moskovkina-sz/0-1/31-1.webp?ts=1758886608" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1426135" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1426133" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1189 #items: array:5 [ 0 => App\Models\Task {#1201 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1425060 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "31" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/7-249" "field_display_title" => "249" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1202 #items: array:1 [ 0 => App\Models\Term {#1036} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1203 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1204 #items: array:1 [ 0 => App\Models\Branch {#1120} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1205 #items: array:2 [ 0 => App\Models\Branch {#1120} 1 => App\Models\Branch {#1124} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1207 #items: array:2 [ 0 => App\Models\Element {#1216 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 1677593 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1217 …2} "task" => array:2 [ …2] "text" => "<p><strong>249.</strong> В сообщающихся сосудах находятся ртуть, вода и масло (см. рисунок). Ртуть находится на одном уровне в обоих сосудах. Площадь сечения сосудов $3 \text{ см}^2$, высота столба воды $10 \text{ см}$. Определите массу масла, находящегося в сосуде.</p>" "img" => array:1 [ …1] ] #original: array:7 [ "id" => 1677593 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1217 …2} "task" => array:2 [ …2] "text" => "<p><strong>249.</strong> В сообщающихся сосудах находятся ртуть, вода и масло (см. рисунок). Ртуть находится на одном уровне в обоих сосудах. Площадь сечения сосудов $3 \text{ см}^2$, высота столба воды $10 \text{ см}$. Определите массу масла, находящегося в сосуде.</p>" "img" => array:1 [ …1] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Element {#1218 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1781441 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1219 …2} "task" => array:2 [ …2] "text" => "<p><strong>Дано:</strong></p><p>Площадь поперечного сечения сосудов: $S = 3 \text{ см}^2$</p><p>Высота столба воды: $h_в = 10 \text{ см}$</p><p>Плотность воды (справочное значение): $\rho_в = 1000 \text{ кг/м}^3$</p><p>Условие: уровни ртути в обоих сосудах одинаковы.</p><p><em>Перевод в систему СИ:</em></p><p>$S = 3 \text{ см}^2 = 3 \cdot 10^{-4} \text{ м}^2$</p><p>$h_в = 10 \text{ см} = 0,1 \text{ м}$</p><p><strong>Найти:</strong></p><p>Массу масла $m_м$.</p><p><strong>Решение:</strong></p><p>Согласно закону сообщающихся сосудов, давление на любом горизонтальном уровне однородной жидкости, находящейся в равновесии, одинаково. В данной задаче в качестве такого уровня выберем границу раздела ртути с водой и маслом. По условию, ртуть в обоих коленах сосуда находится на одном уровне, следовательно, давления, создаваемые столбами воды и масла на поверхность ртути, равны.</p><p>Давление столба воды в левом сосуде (B) на этом уровне рассчитывается по формуле гидростатического давления:</p><p>$P_в = \rho_в g h_в$</p><p>где $\rho_в$ — плотность воды, $\text{g}$ — ускорение свободного падения, $h_в$ — высота столба воды.</p><p>Давление столба масла в правом сосуде (M) на этом же уровне:</p><p>$P_м = \rho_м g h_м$</p><p>где $\rho_м$ — плотность масла, $h_м$ — высота столба масла.</p><p>Так как система находится в равновесии, эти давления равны (атмосферное давление, действующее на открытые поверхности, одинаково и взаимно компенсируется):</p><p>$P_в = P_м$</p><p>$\rho_в g h_в = \rho_м g h_м$</p><p>Сократив обе части уравнения на $\text{g}$, получим:</p><p>$\rho_в h_в = \rho_м h_м$</p><p>Массу масла $m_м$ можно найти через его плотность и объем. Объем столба масла равен произведению площади сечения сосуда $\text{S}$ на высоту столба масла $h_м$:</p><p>$V_м = S \cdot h_м$</p><p>Следовательно, масса масла:</p><p>$m_м = \rho_м V_м = \rho_м S h_м = S (\rho_м h_м)$</p><p>Из условия равенства давлений мы получили, что $\rho_м h_м = \rho_в h_в$. Подставим это выражение в формулу для массы масла:</p><p>$m_м = S \rho_в h_в$</p><p>Теперь мы можем рассчитать массу масла, используя известные величины. Подставим числовые значения в полученную формулу в системе СИ:</p><p>$m_м = (3 \cdot 10^{-4} \text{ м}^2) \cdot (1000 \text{ кг/м}^3) \cdot (0,1 \text{ м}) = 0,03 \text{ кг}$</p><p>Переведем результат в граммы для удобства:</p><p>$0,03 \text{ кг} = 30 \text{ г}$</p><p><strong>Ответ:</strong> масса масла, находящегося в сосуде, равна 30 г.</p>" ] #original: array:6 [ "id" => 1781441 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1219 …2} "task" => array:2 [ …2] "text" => "<p><strong>Дано:</strong></p><p>Площадь поперечного сечения сосудов: $S = 3 \text{ см}^2$</p><p>Высота столба воды: $h_в = 10 \text{ см}$</p><p>Плотность воды (справочное значение): $\rho_в = 1000 \text{ кг/м}^3$</p><p>Условие: уровни ртути в обоих сосудах одинаковы.</p><p><em>Перевод в систему СИ:</em></p><p>$S = 3 \text{ см}^2 = 3 \cdot 10^{-4} \text{ м}^2$</p><p>$h_в = 10 \text{ см} = 0,1 \text{ м}$</p><p><strong>Найти:</strong></p><p>Массу масла $m_м$.</p><p><strong>Решение:</strong></p><p>Согласно закону сообщающихся сосудов, давление на любом горизонтальном уровне однородной жидкости, находящейся в равновесии, одинаково. В данной задаче в качестве такого уровня выберем границу раздела ртути с водой и маслом. По условию, ртуть в обоих коленах сосуда находится на одном уровне, следовательно, давления, создаваемые столбами воды и масла на поверхность ртути, равны.</p><p>Давление столба воды в левом сосуде (B) на этом уровне рассчитывается по формуле гидростатического давления:</p><p>$P_в = \rho_в g h_в$</p><p>где $\rho_в$ — плотность воды, $\text{g}$ — ускорение свободного падения, $h_в$ — высота столба воды.</p><p>Давление столба масла в правом сосуде (M) на этом же уровне:</p><p>$P_м = \rho_м g h_м$</p><p>где $\rho_м$ — плотность масла, $h_м$ — высота столба масла.</p><p>Так как система находится в равновесии, эти давления равны (атмосферное давление, действующее на открытые поверхности, одинаково и взаимно компенсируется):</p><p>$P_в = P_м$</p><p>$\rho_в g h_в = \rho_м g h_м$</p><p>Сократив обе части уравнения на $\text{g}$, получим:</p><p>$\rho_в h_в = \rho_м h_м$</p><p>Массу масла $m_м$ можно найти через его плотность и объем. Объем столба масла равен произведению площади сечения сосуда $\text{S}$ на высоту столба масла $h_м$:</p><p>$V_м = S \cdot h_м$</p><p>Следовательно, масса масла:</p><p>$m_м = \rho_м V_м = \rho_м S h_м = S (\rho_м h_м)$</p><p>Из условия равенства давлений мы получили, что $\rho_м h_м = \rho_в h_в$. Подставим это выражение в формулу для массы масла:</p><p>$m_м = S \rho_в h_в$</p><p>Теперь мы можем рассчитать массу масла, используя известные величины. Подставим числовые значения в полученную формулу в системе СИ:</p><p>$m_м = (3 \cdot 10^{-4} \text{ м}^2) \cdot (1000 \text{ кг/м}^3) \cdot (0,1 \text{ м}) = 0,03 \text{ кг}$</p><p>Переведем результат в граммы для удобства:</p><p>$0,03 \text{ кг} = 30 \text{ г}$</p><p><strong>Ответ:</strong> масса масла, находящегося в сосуде, равна 30 г.</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1425061" "type" => "task" ] "previous" => array:2 [ "refs" => "1425059" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1213 #items: array:1 [ 0 => App\Models\Book {#1056} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1426134" "type" => "book_page" ] ] #original: 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№252 (с. 31)
Условие. №252 (с. 31)
скриншот условия
252. В сообщающиеся сосуды, площади поперечного сечения которых относятся как 1 : 2, налита вода. В узкий сосуд поверх воды долили столб керосина высотой 30 см. На сколько сантиметров повысится уровень воды в широком сосуде?
Решение. №252 (с. 31)
Дано:
Отношение площадей поперечного сечения сосудов: $S_1/S_2 = 1/2$
Высота столба керосина: $h_к = 30$ см
Плотность воды (табличное значение): $\rho_в = 1000$ кг/м³
Плотность керосина (табличное значение): $\rho_к = 800$ кг/м³
$h_к = 30 \text{ см} = 0.3 \text{ м}$
Найти:
Высоту, на которую поднимется уровень воды в широком сосуде: $\Delta h_2$
Решение:
Пусть $S_1$ - площадь поперечного сечения узкого сосуда, а $S_2$ - широкого. По условию $S_2 = 2S_1$.
Когда в узкий сосуд доливают керосин, он вытесняет воду. Уровень воды в узком сосуде опустится на величину $\Delta h_1$, а в широком – поднимется на величину $\Delta h_2$. Поскольку объем воды сохраняется, объем воды, ушедшей из узкого сосуда, равен объему воды, прибывшей в широкий сосуд.
$V_1 = V_2$
$S_1 \cdot \Delta h_1 = S_2 \cdot \Delta h_2$
Подставим соотношение площадей $S_2 = 2S_1$:
$S_1 \cdot \Delta h_1 = 2S_1 \cdot \Delta h_2$
Отсюда находим связь между изменениями уровней воды:
$\Delta h_1 = 2 \Delta h_2$
После установления равновесия, согласно закону сообщающихся сосудов, давление на одном и том же горизонтальном уровне в жидкости должно быть одинаковым. Выберем в качестве такого уровня конечный уровень воды в узком сосуде (то есть границу раздела керосина и воды).
Давление на этом уровне в узком сосуде создается столбом керосина высотой $h_к$:
$p_1 = \rho_к g h_к$
Давление на этом же уровне в широком сосуде создается столбом воды, высота которого равна разности уровней воды в широком и узком сосудах. Эта разность равна $H = \Delta h_1 + \Delta h_2$.
$p_2 = \rho_в g H = \rho_в g (\Delta h_1 + \Delta h_2)$
В состоянии равновесия давления равны: $p_1 = p_2$.
$\rho_к g h_к = \rho_в g (\Delta h_1 + \Delta h_2)$
Сократим на $\text{g}$:
$\rho_к h_к = \rho_в (\Delta h_1 + \Delta h_2)$
Мы получили систему из двух уравнений:
$\begin{cases} \Delta h_1 = 2 \Delta h_2 \\ \rho_к h_к = \rho_в (\Delta h_1 + \Delta h_2) \end{cases}$
Подставим первое уравнение во второе:
$\rho_к h_к = \rho_в (2\Delta h_2 + \Delta h_2)$
$\rho_к h_к = 3\rho_в \Delta h_2$
Выразим искомую величину $\Delta h_2$:
$\Delta h_2 = \frac{\rho_к h_к}{3\rho_в}$
Подставим числовые значения в систему СИ:
$\Delta h_2 = \frac{800 \text{ кг/м³} \cdot 0.3 \text{ м}}{3 \cdot 1000 \text{ кг/м³}} = \frac{240}{3000} \text{ м} = 0.08 \text{ м}$
Переведем результат в сантиметры:
$0.08 \text{ м} = 8 \text{ см}$
Ответ: уровень воды в широком сосуде повысится на 8 см.
Другие задания:
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